Answer:
[tex]Percentage=8.889\times 10^{-13}[/tex]%
Explanation:
From special theory of relativity the dynamic mass m is related with the rest mass [tex]m_{0}[/tex]of the body as
[tex]m=\frac{m_{0} }{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]
Here, c is the speed of light and v is the velocity of object.
Given mass of the golf ball is 120 g.
[tex]m=\frac{120 }{\sqrt{1-\frac{(40)^{2} }{(3\times 10^{8} )^{2} } } }\\m=120(1-\frac{(40)^{2} }{(3\times 10^{8}) ^{2} })^{-\frac{1}{2} } \\[/tex]
Now applying the binomial theorem and solve the above equation.
[tex]m=(1+\frac{1}{2}(\frac{40}{3\times 10^{8} }) ^{2} )\\m=120(1+8.889\times 10^{-15})[/tex]
Therefore, increase in mass is,
[tex]\Delta m=120\times 8.889\times 10^{-15} \\\Delta m=10.6668\times 10^{-13} g[/tex]
Now percentage of increase in mass with rest mass is,
[tex]Percentage=\frac{10.6668\times 10^{-13} g}{120g} \times 100\\Percentage=8.889\times 10^{-13}[/tex]
Therefore, the percentage of increase in mass with rest mass is [tex]Percentage=8.889\times 10^{-13}[/tex].
